Question

answer the statistical measures and create a box and whiskers plot for the following set of data. enter all values as whole numbers or decimals. 5,8,9,12,13,13,14,16,19,19 min: □ q1: □ med: □ q3: □ max: □ create the box plot by dragging the lines: box plot image with x - axis from 0 to 20

Explanation:

Step1: Find Min and Max

Min is the smallest value, Max is the largest.
Data: 5, 8, 9, 12, 13, 13, 14, 16, 19, 19
Min = 5, Max = 19

Step2: Find Median (Med)

Number of data points \( n = 10 \) (even). Median is average of \( \frac{n}{2} \)-th and \( (\frac{n}{2}+1) \)-th terms.
\( \frac{10}{2} = 5 \), \( \frac{10}{2}+1 = 6 \).
5th term: 13, 6th term: 13.
Med = \( \frac{13 + 13}{2} = 13 \)

Step3: Find Q1 (First Quartile)

Lower half: data before median (first 5 terms: 5, 8, 9, 12, 13).
\( n_{\text{lower}} = 5 \) (odd). Q1 is the middle term (3rd term).
3rd term: 9. So Q1 = 9

Step4: Find Q3 (Third Quartile)

Upper half: data after median (last 5 terms: 13, 14, 16, 19, 19).
\( n_{\text{upper}} = 5 \) (odd). Q3 is the middle term (3rd term).
3rd term: 16. So Q3 = 16

Answer:

Min: \( 5 \)
Q1: \( 9 \)
Med: \( 13 \)
Q3: \( 16 \)
Max: \( 19 \)

(For the box - and - whisker plot: The left whisker starts at 5, the left end of the box at 9, the line inside the box at 13, the right end of the box at 16, and the right whisker ends at 19.)